1.6
Chi-square Analysis
The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an o…
Mendel hypothesized that the phenotypic ratio of a monohybrid cross between individuals with a dominant trait, like purple flowers, and a recessive trait, like white flowers, would be approximately three to one provided the alleles are independently assorted.
When there is an assumption that data will fit a certain ratio, like Mendel’s 3:1 prediction, a null hypothesis is established. The null hypothesis assumes that there is no real difference between the expected and observed values and that any apparent differences are due to chance.
Consider a monohybrid cross between twenty tall plants and twenty short plants. The F2 generation of this cross yields 33 tall plants and 7 short plants. This is the observed value.
To test the null hypothesis, a chi-square analysis can be performed. First, create a table with three columns: phenotype, observed value, and expected value. The phenotype and observed values are already known, but the expected values must be calculated.
Calculate the expected values by dividing the total number of plants observed with the total number of expected plants - that is three plus one equals four. So, forty divided by four is ten.
Ten represents the “one” of the expected three to one frequency. Hence, there are ten plants with the recessive “short” gene.
Now, multiply ten by three to obtain the “three” of the expected three to one frequency. Thus, there are thirty plants with the dominant “tall” gene.
Calculate the difference between the observed and expected value in each row and square the results.
Then, divide this value by the expected value in each row and add them all together to obtain the chi-squared value - 1.2.
The degree of freedom, which is defined as the number of values that can vary in the final calculation of a statistic, must also be calculated. Obtain the degree of freedom using this formula, where n is the number of classes, or in this case phenotypes. Here, there is one degree of freedom.
Using the chi-squared value and degree of freedom, obtain the result on the probability chart. Here, 1.2 falls between 1.07 and 1.64. The p-values for these is 0.30 and 0.20, which is greater than 0.05. Thus, the null hypothesis is not rejected, indicating that the alleles for plant height are independently assorted.
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Q1: What is the null hypothesis in chi-square analysis?
The null hypothesis assumes there is no real difference between expected and observed values, and any apparent differences are due to chance. In genetics, this hypothesis is tested using chi-square analysis to determine whether observed data significantly deviate from predicted Mendelian ratios or if variations occur randomly.
Q2: How do you calculate expected values in a chi-square test?
Divide the total number of observed individuals by the sum of the ratio parts to find the base unit. For a 3:1 ratio with 40 total plants, divide 40 by 4 to get 10. Multiply this base unit by each ratio component: 10 × 3 = 30 tall plants and 10 × 1 = 10 short plants as expected values.
Q3: What does the chi-squared value tell you about genetic data?
The chi-squared value measures how much observed data deviate from expected values. Calculate it by finding the squared difference between observed and expected values for each phenotype, then dividing by the expected value and summing all results. A larger chi-squared value indicates greater deviation from the expected ratio.
Q4: How is the degree of freedom determined in chi-square analysis?
Degree of freedom equals the number of phenotypic classes minus one. For a monohybrid cross with two phenotypes (tall and short), the degree of freedom is 2 - 1 = 1. This value represents how many values can vary in the final statistical calculation.
Q5: When do you reject the null hypothesis in a chi-square test?
Reject the null hypothesis when the p-value is less than 0.05, indicating statistically significant differences between observed and expected values. If the chi-squared value exceeds the critical value from the probability table at α = 0.05, the observed inheritance pattern does not follow the expected Mendelian ratio.
Q6: Why is chi-square analysis important for testing Mendelian inheritance?
Chi-square analysis determines whether observed genetic crosses follow predicted Mendelian ratios or if deviations are statistically significant. By comparing observed phenotypic frequencies to expected values, researchers can confirm whether alleles assort independently and validate genetic hypotheses about inheritance patterns and genetic variation.
Q7: What does a p-value greater than 0.05 mean in chi-square results?
A p-value greater than 0.05 means the null hypothesis is not rejected, indicating that observed differences from expected values are likely due to chance alone. This supports the conclusion that the genetic data are consistent with the predicted inheritance pattern, such as independent assortment of alleles.